Math 105/206 - Quiz 4, Mar 13 2015
IMPORTANT: Write your name AND student number somewhere on this sheet.
No calculators, books or notes. Please show your work to get full marks. (10 marks total)
Problem 1 (4 marks)
A population P (t) of mice grows proportionally (= its rate of change is proportional) to the square root
with a constant of proportionality equal to 3. If P (0) = 100, determine P (t).
p
P (t),
Problem 2 (3 marks)
Solve the following first-order separable differential equation
x3 y 0 = y 2 + 1
Problem 3 (3 marks)
Determine whether the following functions are CDFs of
answer, don’t just write ’yes’ or ’no’.

 0
(x + 1)2
F1 (x) =

1
a continuous random variable. Please justify your
if x ≤ −1
if − 1 < x ≤ 0
if x > 0
1
1
F2 (x) = arctan −
π
x